diff --git a/doc/source/whatsnew/v1.1.2.rst b/doc/source/whatsnew/v1.1.2.rst
index b0d375a52f8ac..ad5f647928738 100644
--- a/doc/source/whatsnew/v1.1.2.rst
+++ b/doc/source/whatsnew/v1.1.2.rst
@@ -29,7 +29,7 @@ Bug fixes
 - Bug in :class:`Series` constructor raising a ``TypeError`` when constructing sparse datetime64 dtypes (:issue:`35762`)
 - Bug in :meth:`DataFrame.apply` with ``result_type="reduce"`` returning with incorrect index (:issue:`35683`)
 - Bug in :meth:`DateTimeIndex.format` and :meth:`PeriodIndex.format` with ``name=True`` setting the first item to ``"None"`` where it should bw ``""`` (:issue:`35712`)
--
+- Bug in :meth:`Float64Index.__contains__` incorrectly raising ``TypeError`` instead of returning ``False`` (:issue:`35788`)
 
 .. ---------------------------------------------------------------------------
 
diff --git a/pandas/_libs/index.pyx b/pandas/_libs/index.pyx
index d6659cc1895b1..569562f5b5037 100644
--- a/pandas/_libs/index.pyx
+++ b/pandas/_libs/index.pyx
@@ -80,7 +80,11 @@ cdef class IndexEngine:
             values = self._get_index_values()
 
             self._check_type(val)
-            loc = _bin_search(values, val)  # .searchsorted(val, side='left')
+            try:
+                loc = _bin_search(values, val)  # .searchsorted(val, side='left')
+            except TypeError:
+                # GH#35788 e.g. val=None with float64 values
+                raise KeyError(val)
             if loc >= len(values):
                 raise KeyError(val)
             if values[loc] != val:
diff --git a/pandas/tests/indexes/numeric/test_indexing.py b/pandas/tests/indexes/numeric/test_indexing.py
index 473e370c76f8b..508bd2f566507 100644
--- a/pandas/tests/indexes/numeric/test_indexing.py
+++ b/pandas/tests/indexes/numeric/test_indexing.py
@@ -228,6 +228,12 @@ def test_take_fill_value_ints(self, klass):
 
 
 class TestContains:
+    @pytest.mark.parametrize("klass", [Float64Index, Int64Index, UInt64Index])
+    def test_contains_none(self, klass):
+        # GH#35788 should return False, not raise TypeError
+        index = klass([0, 1, 2, 3, 4])
+        assert None not in index
+
     def test_contains_float64_nans(self):
         index = Float64Index([1.0, 2.0, np.nan])
         assert np.nan in index